ECE 431 Digital Signal Processing Lecture Notes

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ECE 431Digital Signal ProcessingLecture NotesProf. Dan CobbContents1 Introduction22 Review of the DT Fourier De nition and Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Periodic Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 time and Frequency Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . Aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Nyquist Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anti-Aliasing Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Downsampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Upsampling.

analysis of temporal signals makes heavy use of the Fourier transform in one time variable and one frequency variable. Spatial signals require two independent variables. Analysis of such signals relies on the Fourier transform in two frequency variables (e.g. ECE 533). In ECE 431, we will restrict ourselves to temporal signal processing. 2

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